Annulenes Relative energies

Figure 3.13. Origin of the fi contributions to the B term. The broken horizontal lines indicate the energies of the complex MOs in the absence of the magnetic field, the double arrows give the Zeeman splittings and the round arrows show the sense of electron circulation (viewed from the positive z axis). The canonical MOs of the perturbed annulene, whose energies are given by full lines, result from a pairwise mixing of the perimeter MOs, whose relative weights are indicated by the thickness of the round arrows (by permission from Michl, 1978).

In the fused compounds (241) and (242) the furan ring fails to react as a diene and Diels-Alder reaction with dienophiles occurs on the terminal carbocyclic rings. However, (243) and (244) afford monoadducts with dimethyl fumarate by addition to the furan rings (70JA972). The rates of reaction (Table 2) of a number of dehydroannuleno[c]furans with maleic anhydride, which yield fully conjugated dehydroannulenes of the exo type (247), have been correlated with the aromaticity or antiaromaticity of the products (76JA6052). It was assumed that the transition state for the reactions resembled products to some extent, and the relative rates therefore are a measure of the resonance energy of the products. The reaction of the open-chain compound (250), which yields the adduct (251), was taken as a model. Hence the dehydro[4 + 2]annulenes from (246) and (249) are stabilized compared to (251), and the dehydro[4 ]annulenes from (245) and (248) are destabilized (Scheme 84). 

We will not concern ourselves here with the attempt to discern a true definition of aromaticity, nor with the largely unproductive " desire to rank-order relative aromaticity. Rather, we will focus on how computational chemistry has been used to help define two of the criteria of aromaticity. We will discuss how to compute the stabilization energy of an aromatic species and then how we can compute magnetic properties that can be related to aromaticity. We will then conclude with a discussion of how these measures have been employed to investigate the nature of annulenes and the MiUs-Nixon effect. 

Edgar Heilbronner in 1964 worked out that such a twisted system (Mobius system) would be aromatic if it contained 4n conjugated tr-electrons. Curiously, no actual examples were identified until relatively recently, when it was proposed that [12], [16] and [20] annulenes have several higher energy conformations which adopt this mode. In 2003, the first crystal structure of a true stable Mobius [16] annulene was completed, and various heteroannulenes were identified as existing in Mobius form. 

Finally, if the perturbation due to the substituent as well as its position in the molecular framework is known, MCD spectroscopy can be used to investigate the nature and the ordering of the frontier orbitals. In this way, the relative importance of transannular interactions compared to substituent effects and geometrical distortions for the electronic structure of bridged an-nulenes such as l,6-methano[10]annulene (14) may be assessed by determining the energy ordering of the frontier orbitals of substituted derivatives of 14 from their MCD spectra. This is shown in detail in Example 3.12. 

The instability of [4]annulene (a neutral 4n n-electron annulene) can be gleaned from either Frost s Circle or HMO theory. As shown in Fig. 2. the former predicts an open-shell triplet, implicating instability. The latter reports no gain in energy (0 P) relative to its acyclic analogue, butadiene. Experimental evidence shows that cyclobutadiene IS. in fact, a closed shell species, with alternate single and double bonds. Regardless, as predicted. [4]annulene proved to be an unstable compound. 

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